Solutions Manual to accompany An Introduction to Numerical Methods and Analysis, 3rd Edition

CHAPTER 10AN INTRODUCTION TO SPECTRAL METHODS

10.1 SPECTRAL METHODS FOR TWO‐POINT BOUNDARY VALUE PROBLEMS

Exercises:

1. Write a program to solve the BVP
   

   using the spectral method, with either “boundary bordering” or “basis recombination.” The exact solution is

   

   for , , and

   

   (confirm this); plot the solution and the error, and produce a table of maximum absolute errors, for .

   Solution: The author got the solution and error plots in Fig. 10.1 and Fig. 10.2 for .

   

   Figure 10.1 Solution to Problem 1, .

   Figure 10.2 Error for Problem 1, .

2. Solve the BVP in Example 10.2, for , but take ...